The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure

Oksana E. Hentosh , Yarema A. Prykarpatskyy , Aleksandr Balinsky , Anatolij K. Prykarpatsky

Abstract

There are reviewed modern investigations devoted to studying nonlinear dispersiveless heavenly type integrable evolutions systems on functional spaces within the modern differential-geometric and algebraic tools. Main accent is done on the loop diffeomorphism group vector fi elds on the complexifi ed torus and the related Lie-algebraic structures, generating dispersionless heavenly type integrable systems. As examples, we analyzed the Einstein–Weyl metric equation, the modifi ed Einstein–Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations, the inverse fi rst Shabat reduction heavenly equation, the fi rst and modifi ed Plebański heavenly equations,the Husain heavenly equation, the general Monge equation and the classical Korteweg-de Vries dispersive dynamical system. We also investigated geometric structures of a class of spatially one-dimensional completely integrable Chaplygin type hydrodynamic systems, which proved to be deeply connected with differential systems on the complexifi ed torus and the related diffeomorphism group orbits on them.
Author Oksana E. Hentosh
Oksana E. Hentosh,,
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, Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
, Aleksandr Balinsky
Aleksandr Balinsky,,
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, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
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Journal seriesAnnals of Mathematics and Physics, ISSN 2689-7636, e-ISSN 2689-7636, (0 pkt)
Issue year2019
Vol2(1)
Pages11-25
Publication size in sheets0.7
Keywords in EnglishLax–Sato equations; Multi-diemnsional integrable heavenly equations; Lax integrability; Hamiltonian system; Torus diffeomorphisms; Loop lie algebra; Lie-algebraic scheme; Casimir invariants; R-structure; Lie-poisson structure; Conformal structures; Superalgebras; Super-integrable systems
DOIDOI:10.17352/amp.000006
URL https://www.peertechz.com/articles/AMP-2-106.pdf
Languageen angielski
LicenseJournal (articles only); author's original; Uznanie Autorstwa (CC-BY); after publication
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The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure 627,82 KB
Score (nominal)5
Score sourcejournalList
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